They're not picking a side. That's the whole thing. Their position is that it's good to be a patriot and that CK is a type of patriot. There are also the flag-waving type of patriots. Nike will continue to make red, white, and blue gear, they're just backing off Betsy Ross.
This is less for you and just a general statement, but everybody has their complaints about America. Everybody. I don't get why people find CK's complaints so absurd. Yeah, he's got hypocritical positions. So do basically all D's and R's. Trump won complaining about the way America was. Literally, his campaign slogan implied that America was no longer great. We like it when people have the same complaints as us about America, but when we disagree with their complaints, it's "don't like it, then leave."